Show Light Has The Same Velocity in S and S'

1. The problem statement, all variables and given/known data
Consider the velocity transformation equations. Find the x and y components of the velocity in the frame S of a light ray that has speed c along the y′axis of frame S′ where S and S′are the usual frames we have been considering with S′ moving with speed v with respect to S along the common x − x′ axes. Show that the light ray has speed c in the frame S.

2. Relevant equations
1. u'_x = (u_x-v)/{1-(v*u_x/c^2)}
2. u'_y = u_y/{gamma(1-(v*u_x/c^2))}
3. u'_z = u_z/{gamma(1-(v*u_x/c^2))}3. The attempt at a solution
u_z = u'_z = 0, obviously. I'm looking for u_x and u_y, so I need to start with u_x. I set u'_x to 0 and solved, getting u_x = v. I'm not sure if that's right, or if I should've gotten c, but I tried to plug u_x = v into equation 2, and did not get that u_y was c.